To graph the equations y = x-5 and -2x + 2y = -10, we can start by converting the second equation into slope-intercept form.
-2x + 2y = -10
Rearranging the equation:
2y = 2x - 10
Dividing both sides by 2:
y = x - 5
Now we have both equations in slope-intercept form, where y is isolated on one side.
The equation y = x-5 represents a straight line with a slope of 1 and a y-intercept of -5. This means that for every increase of 1 in the x-coordinate, the y-coordinate will increase by 1. The line crosses the y-axis at -5.
The equation -2x + 2y = -10 can be rewritten as y = x + 5, which has the same slope and y-intercept as the previous equation.
To graph these equations, plot the points (-5, 0) and (0, -5) on a graph. Then, draw a straight line passing through these two points. This line is a graph of both equations.